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Some of the distant galaxies appear to be receding from us faster than the speed of light due to stretch of the space between us and those galaxies.

By an analogy with the ant on a rope paradox, the light emitted from those galaxies can actually reach us. Is it true that, at one point of time, those galaxies suddenly disappear from our view, and then after sufficiently large times (which may be more than the lifetime of the universe), they come into view again? And by the same reasoning, would more previously hidden galaxies will become visible at some time?

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I'll answer your question in 2 parts. First, can a galaxy (which we can currently see) suddenly disappear from view for some reason related to the expansion of space?

Let's take a galaxy that we can currently observe. We'll assume that the galaxy has been emitting light forever (since the birth of the Universe) and will keep emitting light forever. We observe it, so some of that light has reached us. If some light has reached us and the galaxy is continuously emitting light, then there must also be some light that is about to reach us, then some more light just a little further away. Let's imagine this as a chain of photons that stretches between the galaxy and us.

For us to suddenly stop being able to observe the galaxy, we would need to break this chain - perhaps this can happen if space expands quickly? It turns out that the chain doesn't actually break, it stretches - each photon gets longer as the space containing it literally expands. This is what we call cosmological redshift. As time goes on the photons reaching us are more and more stretched, so their wavelengths are longer than when they were emitted (and their energies are lower) - they are redder.

There is another way to produce red-shifted light - if the source is moving away from the observer, the doppler effect causes a redshift (often called the doppler redshift). The appearance of a distant galaxy moving away from us faster than the speed of light comes from taking the observed redshift of the galaxy and interpreting it as a doppler redshift - this can give a speed greater than $c$. However, the redshift has 2 components (doppler and cosmic, in practice the cosmic redshift dominates the doppler redshift for very distant galaxies), and one of them is not related to the speed of the source at all, so the "speed limit" is still obeyed.

The second part of your question asked if a galaxy that had disappeared can later reappear. Since a galaxy can't disappear in the first place, the answer is simply no. We can, however, suddenly see a galaxy that we could never have seen before appear. It has been emitting light for a long time, but was so far away that its light had not yet had time to reach us. Once enough time has passed, into view it comes. There can also be galaxies that we will never be able to observe - they are emitting light in our direction, but they are far enough away that the intervening space is expanding fast enough so that the light will never reach us.

In practical terms there are other effects that could cause us to start or stop being able to observe a distant source - the intensity of the source could change with time, or the arriving light could be too dim for our detection equipment - but from a theoretical point of view, I think the answer above covers the possibilities. There is also one more possible source of redshift that I didn't mention - gravitational redshift - that comes out of general relativity.

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This is incorrect. As the universe is accelerating the equivalent of an event horizon will form as space approaches desitter. Eventually we will only be able to see the galaxies in the local group. –  physicsphile Sep 30 '12 at 18:45
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